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Question

Evaluate the following integrals:

3x-2x+12x+3dx

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Solution

Let I=3x-2x+12x+3dxWe express3x-2x+12x+3=Ax+1+Bx+12+Cx+33x-2=Ax+1x+3+Bx+3+Cx+12Equating the coefficients of x2, x and constants, we get0=A+C and 3=4A+B+2C and -2=3A+3B+Cor A=114 and B=-52 and C=-114I=114x+1+-52x+12+-114x+3dx =1141x+1dx-521x+12 dx-1141x+3 dx =114logx+1+52x+1-114logx+3+cHence, 3x-2x+12x+3dx=114logx+1+52x+1-114logx+3+c

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